This invention relates to electrical induction logging systems for determining the nature and characteristics of the various sub-surface formations penetrated by a borehole in the earth. More particularly, this invention relates to a method and system for processing the induction log measurements whereby the non-linear variations in the sonde response function as a function of the conductivity of the formations being investigated and the unwanted contributions to each log measurement from currents flowing in formations spaced apart from the measurement depth are attenuated.
It is important to the oil and gas industry to know the nature and characteristics of the various sub-surface formations penetrated by a borehole because the mere creation of a borehole (typically by drilling) usually does not provide sufficient information concerning the existence, depth location, quantity, etc., of oil and gas trapped in the formations. Various electrical techniques have been employed in the past to determine this information about the formations. One such technique commonly used is induction logging. Induction logging measures the resistivity (or its inverse, conductivity) of the formation by first inducing eddy currents to flow in the formations in response to an AC transmitter signal, and then measuring a phase component signal in a receiver signal generated by the presence of the eddy currents. Variations in the magnitude of the eddy currents in response to variations in formation conductivity are reflected as variations in the receiver signal. Thus, in general, the magnitude of a phase component of the receiver signal, that component in-phase with the transmitter signal, is indicative of the conductivity of the formation.
In theory, the electrical resistivity of the formation should be relatively high (or the conductivity relatively low) when the formation contains a high percentage of hydrocarbons because hydrocarbons are relatively poor conductors of electricity. Where hydrocarbons are not present in the formations and the formations contain salt water, the electrical resistivity of the formation should be relatively low. Formation water, typically salty, is a relatively good conductor of electricity. Induction resistivity logging tools thus obtain information about the formations which can be interpreted to indicate the presence or absence of these hydrocarbons.
U.S. Pat. Nos. 2,582,314; 3,340,464; 3,147,429; 3,179,879 and 3,056,917 are illustrative of typical prior-art well logging tools which utilize the basic principles of induction logging. In each of the tools disclosed in these patents, a signal generator operates to produce an AC transmitter signal which is applied to a transmitter coil. The current in the transmitter coil induces in the formations a magnetic field, which, in turn, causes eddy currents to flow in the formations. Because of the presence of these formation currents, a magnetic field is coupled into a receiver coil R thereby generating a receiver signal. (Logging tools having "a receiver coil" and "a transmitter coil" each comprising several coils arranged in a predetermined geometrical fashion to obtain a desired response are commonly used. These coil systems are sometimes referred to as "focused" coil systems.) The receiver signal is then amplified and applied to one or more phase sensitive detectors (PSDs). Each PSD detects a phase component signal having the same phase as a phase reference signal which is also applied to the detector. The phase reference signal has a predetermined phase relationship to the current in the transmitter coil(s). The output of the PSD(s) may be further processed downhole, or may be sent uphole to surface equipment for processing or display to an operating engineer.
A quantitative determination of the conductivity of the formations is based in large part on the value obtained for the phase component signal that is in-phase with the transmitter current in the transmitter coil. This component signal is commonly referred to as the real or in-phase (R) component. Measurement of a phase component signal which has a phase orthogonal to (or, in quadrature to) the transmitter current is sometimes obtained. This component signal is commonly referred to as the quadrature-phase (X) component signal.
Measurement of both the R and X phase component signals of the receiver signal is known. U.S. Pat. Nos. 3,147,429 and 3,179,879 both disclose induction logging apparatus which detects real and phase quadrature components (designated in those patents as V.sub.r and V.sub.x ', respectively) of the receiver signal from the receiver coil. The tools disclosed in these patents show the output from a receiver amplifier being applied to ideally identical PSD circuits, one for detecting the R component signal and the other for detecting the X component signal. Appropriate phase shifting components are provided for generating the phase quadrature phase reference signals required by the PSDs in order to resolve the phase component signals. Recent advances in the area of digital induction logging apparatus, such as those disclosed in co-pending U.S. patent application Ser. No. 217,367, filed June 8, 1981, which is incorporated herein for all purposes and is entitled "A Digital Induction Logging Tool," have enabled accurate and precise readings of the R and X component signals to be made. Application Ser. No. 271,367 is assigned to the same Assignee as the present application.
In addition to the hardware limitations addressed by the system disclosed in the incorporated patent application, the methods for determining true formation resistivity at any particular depth from induction log measured data have in the prior art been adversely affected in cases where the true conductivity of adjacent bedding formations varies over a wide dynamic range.
To interpret the tool voltage measurements representative of the true formation conductivity requires a sonde response function relating formation conductivity to output voltage measurements of the tool. This sonde response function is typically known as the vertical sensitivity curve of the induction tool sonde. For homogeneous formations, the sonde response function for a typical induction sonde can best be described as a response curve which has a main lobe of finite width from which the majority of the signal originates. Sidelobes to each side of the main lobes with non-zero amplitudes extend longitudinally up and down the borehole from the center of the sonde with decreasing amplitude.
A term widely used by those skilled in the art to describe this sonde response function is the "vertical geometrical factor" of an induction tool. The vertical geometrical factor (GF) is the sonde response function measured in a homogeneous formation having zero conductivity (infinite resistivity). As is discussed below, the character of the sonde response function varies with the conductivity of the formations being investigated. Thus, the GF is a special situation (zero conductivity) for the sonde response function. The condition of zero conductivity is not often encountered in induction logging, although low conductivity formations are regularly encountered. The term, general geometrical factor (GGF), is often used to describe the sonde response function regardless of the conductivity at which a given response curve is obtained.
Because of the non-zero sidelobes of the sonde response function, currents flowing in the formations above and below the sonde provide an unwanted contribution to the log measurements. For example, where the main lobe of the sonde response function is investigating a thin bed of low conductivity, the conductivity measurement will be too large if the thin bed is located near adjacent beds of higher conductivity. This unwanted contribution is referred to by those skilled in the art as the "shoulder effect," and generally is meant to describe the incorrect interpretation of the sonde measurements resulting from the non-zero sidelobes in the sonde response function.
The character of these sidelobes of the sonde response function has in the past been controlled by the geometry of the sonde coupled with the physics of induction logging. Various attempts have been made in the past to minimize these sidelobes, for example, using multiple transmitter and receiver coils arranged in predetermined relationships within the sonde itself. U.S. Pat. Nos. 2,582,314 and 3,067,383 illustrate induction logging sondes in which multiple coils arranged in arrays are used to "focus" the sonde response function response curve to narrow the width of the main lobe and attenuate the sidelobes. U.S. Pat. No. 2,790,138 discloses an induction logging tool in which two separate induction coil arrangements are used, both arrangements having the same geometrical center with an inner transmitter-receiver coil pair physically located between an outer transmitter receiver coil pair. Assuming that both coil pairs have the same sidelobe responses at vertical displacements greater than some fixed distance from the center of the sonde, by subtracting the signal from one coil pair from the other will reduce the effect of the contribution of formations spaced apart from the center of the sonde beginning at the fixed distance outwardly.
These focused coil systems, and such techniques as disclosed in U.S. Pat. No. 2,790,138, have not been able to effectively reduce the sidelobes of the sonde response function to a level which will permit the logging tool to measure the conductivity of the formations accurately over several decades of magnitude. Because of the complexity of these focused coil arrangements, and the problems of mutual coupling and the difficulty in constructing the sonde, resort to more elaborate focused arrangements to further reduce the sidelobes has already reached a point of diminishing returns.
In addition to the shoulder effect phenomenon discussed above, there is yet another problem which limits the ability of the induction logging equipment to accurately obtain a measure of the true conductivity of the formations over a wide dynamic range. This problem is characterized by the non-linear changes in the profile of the sonde response function as a function of formation conductivity. As the conductivity of the formation being investigated increases, the amplitude and shape of both the sonde response function's main lobe and its sidelobes changes, and these changes are non-linear with increasing conductivity. This characteristic is referred to as "skin effect." The skin effect phenomenon has also been described as that error signal which degrades the in-phase component measurement of the conductivity to produce an incorrect value. This skin effect phenomenon results primarily from the mutual interaction with one another of different portions of the secondary current flow in the formation material. The magnitude of this skin effect phenomenon also increases as the system operating frequency increases.
Prior art has shown that, among other things, the magnitude of this skin effect phenomenon is a complex and complicated function of the coil system operating frequency, the effective length of the coil system, and the conductivity value of the adjacent formation material. The last-mentioned factor renders this phenomenon particularly objectionable because it produces the above-mentioned non-linear variation in the output signal of the sonde. The occurrence of these non-linear variations can be substantially eliminated for a large range of formation conductivity values by proper choice of the coil system, operating frequency and the effective coil system length. These factors, however, place undue restraints on the construction and operation of the coil and associated circuits. These restraints, in turn, limit other desirable features of the coil system apparatus. For example, it is frequently desired that the coil system be able to accurately determine the conductivity value of the formation material in a region lying at a substantial lateral distance from the borehole. This requires a relatively large coil spacing or coil system length. A large spacing, however, increases the percentage of non-linearity resulting from the occurrence of skin effect. As another example of undesirable restraint, the signal-to-noise ratio of the induction logging apparatus can be improved by increasing the tool's operating frequency. This, however, also increases the skin effect non-linearity.
If the conductivity of the formations being investigated is near zero, the GF response curve yields values of conductivities that are free of the skin effect phenomenon. But at higher conductivities, the skin effect, as reflected as a change in the sonde response function, causes the conductivity values obtained from the measurements of the tool to be in error. U.S. Pat. No. 3,147,429 characterizes this skin effect error as a voltage which subtracts from the "geometrical factor" signal predicted by the linear theory on which the GF response curve is based and which is well-known in the art. U.S. Pat. No. 3,147,429 also discusses the skin effect phenomena as it relates to the quadrature-phase component X of each conductivity measurement. Those skilled in the art have recognized that the magnitude of the X component is a function of the conductivity value of the formation material being investigated.
The logging system of U.S. Pat. No. 3,147,429 assumes that, to a degree, the magnitude of the quadrature-phase component measurement X is equal to the magnitude of the skin effect error signal. Since the skin effect error signal tends to decrease the measurement from that which would obtain if the GF were the proper response curve for the formations being investigated, the in-phase component measurements can be corrected by adding an adjusted quadrature-phase component where the adjustment is made dependent on the magnitude of the X component. While this approach yields some correction to the in-phase component measurement for the skin effect error, there is no attention given in the prior art to the origin within the formation from where the skin effect error signal originates. Rather, the prior art corrects for skin effect based only on the magnitude of the component of the conductivity measurement itself. In other words, the spatial aspects of the skin effect error signals are totally ignored by the prior art.
As shown in the case of the shoulder effect phenomenon previously discussed, a consideration of the spatial aspects of the system transfer function is important if a true and accurate measurement of the formation conductivity over a wide dynamic range of conductivities is to be obtained. The skin effect error also has a spatial aspect, because the conductivity of the formations being investigated may not be homogeneous throughout or that the formations adjacent the borehole may be invaded by the drilling mud. The shape and character of the spatial response function for the skin effect error signal can be defined as the difference between the GF response curve and the sonde response curves as measured at different values of conductivity. For these curves, it can be seen that the contributions of formations longitudinally displaced along the borehole from the point of the measurement contribute varying amounts to the skin effect error signal, even when a homogeneous medium is assumed. A gross adjustment to the in-phase component measurement based on a pure magnitude reading for the quadrature-phase component is not adequate to compensate for the skin effect phenomenon so as to permit accurate measurements of the true conductivity over a wide dynamic range in conductivity. Attention must be given to compensating the in-phase measurement based on the contributions to the skin effect error coming from the various parts of the formations.
Thus, it would be advantageous to provide a method of processing the induction log measurements and a system therefor that reduces the unwanted contributions in the log measurements from currents flowing in formations spaced apart from the measurement depth by minimizing the sidelobes in the resulting system response function used to translate the formation conductivity values into the processed measurements. It would also be advantageous to provide a method of processing the induction log measurements to minimize the effects of the non-linear variations in the sonde response function resulting from changes in the conductivity of the formations being investigated.